According to folks who study this sort of thing, up to 40% of internet searches are about medical or health questions or topics. That seems about right to me!
I get a lot of questions regarding the interface between medicine and net based information. I used to give patients a list of specific websites, but it became impossible for me to keep it up to date.
Generally, you should not feel abashed about researching on the internet or asking about your findings. There can't be anything wrong with being seriously interested in your own body and your own health!
At the same time, you should be just as critical or inquiring of internet based sources of information as you would for any other medium such as TV, books, magazines, newspaper or word of mouth. In other words, don't judge a book by its cover. Anyone with a modest level of computer skills can produce a very polished looking responsive website. Do not assume that a finished appearing website with a fast server is necessarily a good source of information.
Websites representing professional medical opinion should reflect this, while those representing personal opinions or chat rooms should be distinctly so. In other words, the Mayo Clinic's website very clearly represents a professional institution while the website of a person who has a specific condition such as M.S. will be representing their personal outlook and experiences. Both may be useful to you, but should be read with the author's background and point of view in mind.
It is difficult to use the internet deductively rather than inductively. That is, looking up a specific known diagnosis such as iron deficiency anemia will yield a wealth of information on that subject. Searching a collection of symptoms such as tiredness and fatigue and dizziness can lead to an overwhelming list of possible diagnoses which could include iron deficiency anemia, but also brain cancer, lupus, syphilis and diabetes.
In other words, trying to diagnose using the internet is difficult. But then, if it was easy medicine would not be defined as a profession!